By using the mathematical hull form and the simple sink propeller model, the mechanism of the free surface effect on the propulsive performance of a ship is elucidated. This sink propeller model is different from the actuator disk model, because the strength of the sink is, determined by the boundary condition at the propeller plane. The hull form is represented by the Michell source distribution. Following results are obtained. 1) This propeller model explains the propeller characteristics under the free surface. 2) The hull wake increases the thrust and the propeller wave wake decreases the thrust. 3) Increase of wave pattern resistance expresses a part of the thrust diminution. 4) It is preferable to analyse the propulsive performance of a ship in the ballast condition by using the propeller characteristics which was obtained at the same F (=V/√gI) . 5) The wave pattern resistance of the self-propelled ship depends on the distance between the hull and the propeller and on Froude number and immersion. 6) As Froude number increases, the wake fraction and the thrust deduction fraction generally undulate under the free surface effect. 7) The ratio of the increase of wave pattern resistance to the thrust of the model ship is nearly same as that of the full-scale ship.